AP{an}中d≠0,a1,a3,a9成等比,求a1+a3+a9/a2+a4+a10

问题描述:

AP{an}中d≠0,a1,a3,a9成等比,求a1+a3+a9/a2+a4+a10

a3=a1+2da9=a1+8da3/a1=a9/a3(a1+2d)/a1=(a1+8d)(a1+2d)4d^2-4a1d=0d(d-a1)=0因为d≠0所以d-4a1=0d=a1a3=3a1,a2=2a1,a4=4a1,a9=9a1,a10=10a1a1+a3+a9/a2+a4+a10=(1+3+9)a1/(2+4+10)a1=13/16